A lathe has two workpiece spindles (28, 30) rotatively mounted each in a headstock (24, 26) and movable therewith in the direction of and transversely to the axis of the spindle. The workpiece clamping means of the spindles (28, 30) face each other. Tool holders (32, 34) are fixedly mounted at the front side of the lathe. In a front working area, the workpieces (46) are shaped exclusively by the displacement of the spindles (28, 30) in the X and Z directions, in cooperation with the tool holders (32, 34). In a transfer position located further back on the guides (12, 14), they are then directly transferred, i.e. without any reversing means, from a spindle (28) to the other (30). Still further back, they are taken up by a conveyor arrangement (44) or delivered to a conveyor arrangement (50).